Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-9x+7y &= -4 \\ 5x-5y &= 6\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-5y = -5x+6$ Divide both sides by $-5$ to isolate $y$ $y = {x - \dfrac{6}{5}}$ Substitute this expression for $y$ in the first equation. $-9x+7({x - \dfrac{6}{5}}) = -4$ $-9x + 7x - \dfrac{42}{5} = -4$ Simplify by combining terms, then solve for $x$ $-2x - \dfrac{42}{5} = -4$ $-2x = \dfrac{22}{5}$ $x = -\dfrac{11}{5}$ Substitute $-\dfrac{11}{5}$ for $x$ back into the top equation. $-9( -\dfrac{11}{5})+7y = -4$ $\dfrac{99}{5}+7y = -4$ $7y = -\dfrac{119}{5}$ $y = -\dfrac{17}{5}$ The solution is $\enspace x = -\dfrac{11}{5}, \enspace y = -\dfrac{17}{5}$.